Wigner Theory Research Articles

Dipolar and contact processes in H2 o-p conversion on ionic surfaces

Different channels in the ortho-para conversion of hydrogen molecules physisorbed on a transition metal oxide surface are investigated. The Wigner process, which assumes catalysts to be point dipoles, is analysed and compared to the dipolar and contact processes, which include the orbital degrees of freedom of the surface electrons. Three possible ground states, corresponding to different surface structures, are considered and their relative efficiencies discussed. In particular, the o-p conversion rate is found to be very sensitive to the presence of a metal dangling bond perpendicular to the surface. The molecule-metal electron overlap is shown to strengthen the contact process considerably but the dipolar one only negligibly. Our general expressions are illustrated by a simple model, corresponding qualitatively to chromium impurities dispersed on an alumina surface and discussed in terms of two parameters: the surface-molecule distance d, and the effective metal nuclear charge Z. A fluctuation of about 100% in the o-p conversion rates, when compared to the original Wigner theory, is found.

Physical conversion of H 2 adsorbed on Cr 2O 3/Al 2O 3

The magnetic interaction of a hydrogen molecule physisorbed on a chromia / alumina catalyst is presented and the influence of the Cr3d dangling bond on the ortho-para hydrogen conversion stressed. The Wigner process, which assumes catalyst point dipoles, is analyzed and compared to the magnetic dipolar process which includes the orbital degrees of freedom of the surface electrons. The surface-molecule distance dependences of the investigated processes are compared and the relative efficiencies of the different surface orbitals stressed. The conversion rate is found to be increased by a factor of between 2 and 9, as compared to the original Wigner theory.

Effective interactions involving massive and massless particles of spin 1/2, 1, 3/2, and 2

The Bargman–Wigner theory is used in order to quantize and build interactions ‘‘à la Fermi’’between massive or massless particles with spin 1/2 , 1, (3)/(2) , and 2.

Quantum tunneling and thermal activation in the parametric oscillator.

The mean time taken for the degenerate parametric oscillator to quantum tunnel between its two above-threshold stable states is calculated in the large photon-number limit. The result is compared with an earlier approximate result using a truncated Fokker-Planck equation in the Wigner representation. This earlier theory is equivalent to stochastic electrodynamics. Our quantum theory results indicate orders of magnitude faster tunneling far above threshold, when compared to the truncated Wigner theory.

Symmetry versus degree of level repulsion for kicked quantum systems

Quantum systems capable of chaotic motion in the classical limit can display linear, quadratic, or quartic level repulsion. For a given (time independent or time dependent) Hamiltonian the degree of level repulsion is determined by the full group of its unitary and antiunitary symmetries. We establish this connection for kicked systems, using Wigner's theory of corepresentations, and the appropriate generalization of Pechukas' phase space flow. We illustrate the theory in terms of two systems of kicked spins both of which are time reversal invariant, one showing linear and the other quadratic level repulsion.

On quantum trajectories and an approximation to the Wigner path integral

In this paper we suggest an approximation to the Wigner Path integral using quantum trajectories. We discuss the results in terms of Bohm’s theory and Takabayasi’s study of the relation between Bohm and Wigner theory. We discuss how this new approach is an approximation to Bohm’s theory and discuss its validity. We also suggest a method of evaluation and where such an approach would be useful.

A revised diagrammatic technique for the degenerate Anderson model

The Goldstone diagrammatic technique developed by Keiter and Kimball for single impurity Anderson model is reformulated. Instead of having the self-energy functions defined on the real axis as the Brillouin–Wigner theory, we have defined the functions on the complex plane. This avoids the complicated and cumbersome regularization procedure required in the Keiter and Kimball formulation. Most important of all it makes the numerical calculations possible. The exact partition function may be written down in terms of irreducible self-energy diagrams. The Green function and spectral function are derived.

Comment on the detailed balance symmetrization procedure of classical spectra

By means of the Wigner theory we derive an expression for the first approximation with respect to ħ of the spectrum related to a general correlation function and its zero-th moment. We then show that the symmetrization of spectra with simply the application of the detailed balance term to the classical spectra is valid in general only for ω ≪ 2kT/ħ .

Hydrogen activation on zinc oxide

Three types of hydrogen adsorption have previously been characterized on zinc oxide at low temperatures, designated Types I, II and III. One of these, Type III, is a molecular form of adsorption which can be specifically titrated by nitrogen adsorption on 10–20% of the surface with formation of a molecular nitrogen species. This selective titration by a molecular nitrogen adsorption was employed to study the participation of molecularly adsorbed hydrogen in the allotropie (ortho-para) hydrogen conversion and isotopic (H 2D 2) hydrogen exchange. The promotional effect of oxygen on the conversion reaction was also investigated. These results at low temperatures clearly indicate that the conversion reaction proceeds predominantly by a molecular paramagnetic mechanism involving this type III hydrogen below 140 °K, while the exchange reaction proceeds via a Bonhoeffer-Farkas mechanism involving type I hydrogen at both low temperature and also at room temperature. At low temperatures, the exchange and conversion reactions are independent, but this is not necessarily true at room temperature. A mathematical model is presented for the paramagnetic conversion based on Wigner's theory involving longer times of interaction. The result is an enhancement of the conversion rate by several orders of magnitude with the deuterium conversion being enhanced more than the molecular hydrogen conversion.

Low temperature parahydrogen enrichment catalysed by paramagnetic ions supported on rutile

Transition metal and lanthanoid ions supported on rutile have been used as catalysts for parahydrogen enrichment at 77 and 90 K. Activities, expressed in molecules ion–1 s–1, varied with the square of the magnetic moment of the cation. The results are explained by Wigner's theory extended to cover conversion proceeding during vibrational motion in the physically adsorbed state.

Optical anomalous dispersion of helium

On the basis of a semiclassical approach, the dynamic polarizability and the index of refraction of helium near 11S–21P resonance are calculated. The steady-state solution of the Schrödinger equation used is well behaved at resonance; hence the decay width, in the Weisskopf and Wigner theory, need not be introduced. The result agrees, in essence, with the results of the Weisskopf and Wigner theory if the irradiance is weak. For great irradiance, the results differ significantly over a broad range of frequencies.

Neutron resonance spectroscopy:Gd154,158,160

Neutron time of flight spectroscopy measurements were made for a range of sample thickness on the even separated Gd isotopes $A=154, 158, \mathrm{and} 160$. These include transmission measurements using 200 and 40 m flight paths and self-indication measurements using a 40 m flight path. Resonance parameters were obtained for 48 levels to 1 keV for $^{154}\mathrm{Gd}$ and for 95 and 56 levels to 10 keV for $^{158}\mathrm{Gd}$ and $^{160}\mathrm{Gd}$. The experimental $s$-wave strength functions were $10^{4}S_{0}=(2.0\ifmmode\pm\else\textpm\fi{}0.3), (1.5\ifmmode\pm\else\textpm\fi{}0.2), \mathrm{and} (1.8\ifmmode\pm\else\textpm\fi{}0.4)$, respectively. For $^{160}\mathrm{Gd}$, the $p$ strength function is $10^{4}S_{1}\ensuremath{\approx}1.7\ifmmode\pm\else\textpm\fi{}0.3$. Essentially complete $s$-wave populations were obtained for the first 19 levels in $^{154}\mathrm{Gd}$ with $〈D〉=14.5\ifmmode\pm\else\textpm\fi{}1.5$ eV and ${\ensuremath{\Delta}}_{\mathrm{exp}}=0.22$ (vs ${\ensuremath{\Delta}}_{\mathrm{DM}}=0.28\ifmmode\pm\else\textpm\fi{}0.11$); 47 levels in $^{158}\mathrm{Gd}$ with $〈D〉=86\ifmmode\pm\else\textpm\fi{}4$ eV and ${\ensuremath{\Delta}}_{\mathrm{exp}}=0.29$ (vs ${\ensuremath{\Delta}}_{\mathrm{DM}}=0.38\ifmmode\pm\else\textpm\fi{}0.11$); and 20 levels in $^{160}\mathrm{Gd}$ with $〈D〉=202\ifmmode\pm\else\textpm\fi{}20$ and ${\ensuremath{\Delta}}_{\mathrm{exp}}=0.32$ (vs ${\ensuremath{\Delta}}_{\mathrm{DM}}=0.30\ifmmode\pm\else\textpm\fi{}0.11$). Comparison of the observed ${\ensuremath{\Gamma}}_{n}^{0}$ distributions with the Porter-Thomas theory and the observed level spacings with the Wigner theory and other statistical orthogonal ensemble tests gave good results for the energy intervals over which complete $s$ populations were observed. The average radiation widths were $〈{\ensuremath{\Gamma}}_{\ensuremath{\gamma}}〉=88$ meV determined from $n=25$ levels in $^{154}\mathrm{Gd}$, $〈{\ensuremath{\Gamma}}_{\ensuremath{\gamma}}〉=105$ meV ($n=27$) in $^{158}\mathrm{Gd}$ and $〈{\ensuremath{\Gamma}}_{\ensuremath{\gamma}}〉=11$ meV ($n=4$) in $^{160}\mathrm{Gd}$.NUCLEAR REACTIONS $^{154,158,160}\mathrm{Gd}(n,n)$, ($n,\ensuremath{\gamma}$), $E=0\ensuremath{-}10$ keV; measured ${\ensuremath{\sigma}}_{t} (E)$; deduced ${E}_{0}$, ${\ensuremath{\Gamma}}_{n}$, ${\ensuremath{\Gamma}}_{\ensuremath{\gamma}}$, ${S}_{0}$, $〈{D}_{0}〉$, ${S}_{1}$.

Parahydrogen conversion on X zeolites

Parahydrogen conversion catalysed by X zeolites containing Na +, H +, and rare earth ions has been investigated over the temperature range 77–610 K. At low temperatures, conversion proceeds by a physical mechanism in which the activity is determined by rare earth ions and paramagnetic impurities. At 77 and 90 K it has been shown that the activity at 7 Torr varies with the square of the magnetic moment of the rare earth ion, demonstrating the applicability of Wigner's theory to physical conversion within zeolites. At high temperatures, conversion proceeds by a chemical mechanism which is associated with the alumino-silicate framework of the zeolite.

Calculation of Chemical Reaction Rates by the R-Matrix Method

The application of Wigner and Eisenbud's R-matrix theory to chemical reactions is tested by calculation of reaction probabilities in collinear H+H2 collisions. Conclusions are drawn concerning resonances, statistical reaction theories, and the calculation of reaction cross sections.

Crystal Field Theory And Magnetic Point Groups

The author's previous work on the application of Wigner's theory of the coreps of non-unitary groups to the Shubnikov groups (magnetic groups) is here considered in relation to crystal field theory. Both the splitting of the energy levels and the symmetry properties of the wave function are considered in magnetic point groups. Examples of 4'mm' and 4m'm' are studied.

R-matrix theory of molecular collisions

The use of Wigner and Eisenbud's R-matrix theory for molecular collisions is discussed. A model of harmonic oscillators is proposed; in this model the activated complex has one negative normal frequency. An example is calculated. The results show that for certain parameters of the potential energy function the experimental order of magnitude for the steric factor is obtained. When the range of the interacting potential increases, quite narrow Breit-Wigner resonances result.

Variational method for molecular re-arrangement collisions

Wigner and Eisenbud's R-matrix theory develops the wave function of the ‘compound molecule region’ in terms of an orthogonal set of functions. This fact suggests the use of a variational method. The method yields approximate solutions at low energies. Some results for the head-on H2 + H collision are quoted.

Proton-neutron magnetic moment ratio in Wigner's theory of supermultiplets

Proton-neutron magnetic moment ratio in Wigner's theory of supermultiplets

Proton-neutron magnetic moment ratio in Wigner's theory of supermultiplets

Proton-neutron magnetic moment ratio in Wigner's theory of supermultiplets

Multi-level analysis of resonances in6Li(d, ) and7Li(p, ) reactions

e resonances observed in 6Li(d, α)α reactions have been fitted using the multi-level formalism of Wigner and Eisenbud's R-matrix theory. Three levels in 8Be around 22 MeV excitation are predicted at excitation energies of 22.542, 24.02 and 25.227 MeV having spins 2+, 0+ and 2+ respectively. The 0+ level has a large deuteron width which is about 75% of the Wigner limit while the two 2+ levels show smaller deuteron widths, about 25% and 3% of the Wigner limit for the lower and higher levels respectively. The alpha reduced widths for all these levels are small compared with the Wigner limit, the 0+ level having the maximum alpha width. The use of this reaction as a detector of polarized deuterons is discussed. Preliminary analysis of the 7Li(p, α)α resonances is also presented.